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International audience; Sparsity-based methods, such as wavelets, have been the state of the art for more than 20 years for inverse problems before being overtaken by neural networks. In particular, U-nets have proven to be extremely effective. Their main ingredients are a highly nonlinear processing, a massive learning made possible by the flourishing of optimization algorithms with the power of computers (GPU) and the use of large available datasets for training. It is far from obvious to say which of these three ingredients has the biggest impact on the performance. While the many stages of nonlinearity are intrinsic to deep learning, the usage of learning with training data could also be exploited by sparsity-based approaches. The aim of our study is to push the limits of sparsity to use, similarly to U-nets, massive learning and large datasets, and then to compare the results with U-nets. We present a new network architecture, called learnlets, which conserves the properties of sparsity-based methods such as exact reconstruction and good generalization properties, while fostering the power of neural networks for learning and fast calculation. We evaluate the model on image denoising tasks. Our conclusion is that U-nets perform better than learnlets on image quality metrics in distribution, while learnlets have better generalization properties.

The Euclid mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. We expand and adjust the mock Euclid likelihoods of the MontePython software in order to match the exact recipes used in previous Euclid Fisher matrix forecasts for several probes: weak lensing cosmic shear, photometric galaxy clustering, the cross-correlation between the latter observables, and spectroscopic galaxy clustering. We also establish which precision settings are required when running the Einstein-Boltzmann solvers CLASS and CAMB in the context of Euclid. For the minimal cosmological model, extended to include dynamical dark energy, we perform Fisher matrix forecasts based directly on a numerical evaluation of second derivatives of the likelihood with respect to model parameters. We compare our results with those of other forecasting methods and tools. We show that such MontePython forecasts agree very well with previous Fisher forecasts published by the Euclid Collaboration, and also, with new forecasts produced by the CosmicFish code, now interfaced directly with the two Einstein-Boltzmann solvers CAMB and CLASS. Moreover, to establish the validity of the Gaussian approximation, we show that the Fisher matrix marginal error contours coincide with the credible regions obtained when running Monte Carlo Markov Chains with MontePython while using the exact same mock likelihoods. The new Euclid forecast pipelines presented here are ready for use with additional cosmological parameters, in order to explore extended cosmological models., 45 pages, 24 figures

Context. The Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) is an ongoing deep photometric multiband survey of the northern sky. As part of UNIONS, the Canada-France Imaging Survey (CFIS) provides r-band data, which we use to study weak-lensing peak counts for cosmological inference. Aims. We assess systematic effects for weak-lensing peak counts and their impact on cosmological parameters for the UNIONS survey. In particular, we present results on local calibration, metacalibration shear bias, baryonic feedback, the source galaxy redshift estimate, intrinsic alignment, and cluster member dilution. Methods. For each uncertainty and systematic effect, we describe our mitigation scheme and the impact on cosmological parameter constraints. We obtain constraints on cosmological parameters from Monte Carlo Markov chains using CFIS data and MassiveNuS N-body simulations as a model for peak counts statistics. Results. Depending on the calibration (local versus global, and the inclusion or not of the residual multiplicative shear bias), the mean matter density parameter, Ωm, can shift by up to −0.024 (−0.5σ). We also see that including baryonic corrections can shift Ωm by +0.027 (+0.5σ) with respect to the dark-matter-only simulations. Reducing the impact of the intrinsic alignment and cluster member dilution through signal-to-noise cuts leads to larger constraints. Finally, with a mean redshift uncertainty of ∆z¯ = 0.03, we see that the shift in Ωm (+0.001, which corresponds to +0.02σ) is not significant. Conclusions. This paper investigates, for the first time with UNIONS weak-lensing data and peak counts, the impact of systematic effects. The value of Ωm is the most impacted and can shift by up to ∼ 0.03, which corresponds to 0.5σ depending on the choices for each systematics. We expect constraints to become more reliable with future (larger) data catalogs, for which the current pipeline will provide a starting point. The code used to obtain the results is available on GitHub., Astronomy & Astrophysics, 671, ISSN:0004-6361, ISSN:1432-0746

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starletl1-norm. Peak counts are the local maxima in the map, andl1-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ωm, the reduced Hubble constant h, the matter fluctuation amplitude σ8, and the dark energy equation of state parameter w0. In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and thel1-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined., Astronomy & Astrophysics, 672, ISSN:0004-6361, ISSN:1432-0746

Supervised Dictionary Learning has gained much interest in the recent decade and has shown significant performance improvements in image classification. However, in general, supervised learning needs a large number of labelled samples per class to achieve an acceptable result. In order to deal with databases which have just a few labelled samples per class, semi-supervised learning, which also exploits unlabelled samples in training phase is used. Indeed, unlabelled samples can help to regularize the learning model, yielding an improvement of classification accuracy. In this paper, we propose a new semi-supervised dictionary learning method based on two pillars: on one hand, we enforce manifold structure preservation from the original data into sparse code space using Locally Linear Embedding, which can be considered a regularization of sparse code; on the other hand, we train a semi-supervised classifier in sparse code space. We show that our approach provides an improvement over state-of-the-art semi-supervised dictionary learning methods.

In astronomy, upcoming space telescopes with wide-field optical instruments have a spatially varying point spread function (PSF). Specific scientific goals require a high-fidelity estimation of the PSF at target positions where no direct measurement of the PSF is provided. Even though observations of the PSF are available at some positions of the field of view (FOV), they are undersampled, noisy, and integrated into wavelength in the instrument's passband. PSF modeling represents a challenging ill-posed problem, as it requires building a model from degraded observations that can infer a super-resolved PSF at any wavelength and position in the FOV. Our model, coined WaveDiff, proposes a paradigm shift in the data-driven modeling of the point spread function field of telescopes. We change the data-driven modeling space from the pixels to the wavefront by adding a differentiable optical forward model into the modeling framework. This change allows the transfer of complexity from the instrumental response into the forward model. The proposed model relies on stochastic gradient descent to estimate its parameters. Our framework paves the way to building powerful, physically motivated models that do not require special calibration data. This paper demonstrates the WaveDiff model in a simplified setting of a space telescope. The proposed framework represents a performance breakthrough with respect to the existing state-of-the-art data-driven approach. The pixel reconstruction errors decrease 6-fold at observation resolution and 44-fold for a 3x super-resolution. The ellipticity errors are reduced at least 20 times, and the size error is reduced more than 250 times. By only using noisy broad-band in-focus observations, we successfully capture the PSF chromatic variations due to diffraction. Code available at https://github.com/tobias-liaudat/wf-psf., Comment: Submitted. Without appendix: 42 pages, 10 figures, 4 tables